Question

please help !! A safety regulation states that the height h of a guardrail should be 106 centimeters with an absolute deviation of no more than 7 centimeters. Write and solve an absolute value inequality that represents the acceptable heights of a guardrail. The absolute value inequality is_ . The acceptable range of heights of a guardrail are _cm to _cm.

Answer 1

The absolute value is the mean value itself therefore the absolute value is 106 centimeters.

The acceptable range can be obtained by adding and subtracting the absolute deviation on the mean, that is:

106 cm ± 7 cm so that:

The acceptable range of heights are 99 cm to 113 cm.

Answer 2

The height h of a guardrail = 106 centimeters

absolute deviation =  7 centimeters

To find the acceptable heights of a guardrail , we add and subtract absolute deviation(7) from the mean height(106)

The acceptable range of height is 7 cm away from 106 to the left and then to the right.

106 + 7 = 113

106 - 7 = 99

acceptable heights are defined by

99 <=h<=113

The absolute value inequality is |x-106|<=7

The acceptable range of heights of a guardrail are 99 cm to 113 cm.